Question: Solve for $x$ and $y$ using elimination. ${-4x+6y = -2}$ ${5x-5y = 15}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $4$ ${-20x+30y = -10}$ $20x-20y = 60$ Add the top and bottom equations together. $10y = 50$ $\dfrac{10y}{{10}} = \dfrac{50}{{10}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-4x+6y = -2}\thinspace$ to find $x$ ${-4x + 6}{(5)}{= -2}$ $-4x+30 = -2$ $-4x+30{-30} = -2{-30}$ $-4x = -32$ $\dfrac{-4x}{{-4}} = \dfrac{-32}{{-4}}$ ${x = 8}$ You can also plug ${y = 5}$ into $\thinspace {5x-5y = 15}\thinspace$ and get the same answer for $x$ : ${5x - 5}{(5)}{= 15}$ ${x = 8}$